300 TeV photon from GRB 221009A: A hint at nonlinear Lorentz invariance violation?

The air shower array Carpet-3 detected a 300 TeV photon from the direction of GRB 221009A at 4536 s after the Fermi Gamma-ray Burst Monitor trigger for this event. If the association with this gamma-ray burst is real, then it poses two puzzles. First, why was this photon not absorbed by the extragalactic background light? ``New physics'' beyond the Standard Model is required to explain how it managed to reach Earth from a cosmological distance. Second, why was this photon detected when the very high energy (VHE) afterglow observed by the Large High Altitude Air Shower Observatory (LHAASO) already faded? A novel astrophysical mechanism is required to explain this delay. In this work we show that Lorentz invariance violation (LIV), which arises as a low-energy limit of certain quantum gravity theories, can solve both puzzles. It shifts thresholds of particle interaction and changes the opacity of the extragalactic background, and causes energy-dependent variations of the photon velocity, which changes the photon time of flight. We investigate the LIV parameter space assuming that the 300 TeV photon is a part of the VHE afterglow detected by the LHAASO in the TeV range. We identify viable solutions and place stringent two-sided constraints on the LIV energy scale required to resolve the observational puzzles. First-order LIV appears to be incompatible with the constraints set by analyzing the TeV afterglow of this gamma-ray burst. Viable solutions emerge for higher orders. In particular, the commonly studied second-order subluminal LIV with ${E}_{\mathrm{LIV}2}=1.3{0}_{\ensuremath{-}0.35}^{+0.56}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}{E}_{\mathrm{Pl}}$ (95.4% credibility level; ${E}_{\mathrm{Pl}}$ is the Planck energy) is consistent with all the observed data.